Hello,

I have simulated a simple rectangular waveguide (WR-90) using CST Studio Suite  , with a thickness of 1 mm, operating at a frequency of 9.6 GHz. The guided wavelength for this configuration is approximately λg≈42.34 mm, and the initial length of my waveguide is L=42.34 mm

The S21 phase for this configuration is approximately -0.6 degrees, which is within an acceptable range.

When I increased the length to 5×42.34 mm=211.7 mm, the S21 phase shifted to about -3 degrees (calculated as 5×−0.6=−3), which is also acceptable.

However, upon further increasing the length to 950 mm (calculated as 22.437×42.34), the CST simulator reported an S21 phase of approximately -175 degrees. This result is concerning, as I expected the phase to follow the same linear relationship (i.e., 22.437×−0.6=−13.462), which would have been acceptable.

Additionally, I noticed significant variability in results when changing the mesh cell size from 15 to 25. For this relatively simple structure, I anticipated that an acceptable mesh size of 20 or 25 would yield consistent results. However, the S21 phase varied dramatically from -163 to -175 degrees, which is unexpected.

Besides,According to my calculations, the S21 phase should be: Δφ = ((2π) / λ_g) × L = (360° / 42.34) × 950 = 8077° Since the wave cycle is 360°, I removed all multiples of 360°, so: Δφ = 157.46°

As add the phase difference of -.6 to above calculation: -13.462 (22.437×−0.6) so: Δφ = 157.46°-13.462=144°

However, the CST simulator shows an S21 phase of approximately -175°. Because the phase in CST varies between -180° and 180°, -175° is equal to 355°. So they are different.

Could you help me identify where my mistake might be? I'm eager to understand this discrepancy and improve my simulation results. Thank you!